αS from Fπ and renormalization group optimized perturbation theory

A variant of variationally optimized perturbation, incorporating renormalization group properties in a straightforward way, uniquely fixes the variational mass interpolation in terms of the anomalous mass dimension. It is used at three successive orders to calculate the nonperturbative ratio F pi/(Lambda) over bar of the pion decay constant and the basic QCD scale in the (MS) over bar scheme. We demonstrate the good stability and ( empirical) convergence properties of this modified perturbative series for this quantity, and provide simple and generic cures to previous problems of the method, principally the generally nonunique and nonreal optimal solutions beyond lowest order. Using the experimental F-pi input value we determine (Lambda) over bar (n)f=2 similar or equal to 359(-25)(+38) +/- 5 MeV and (Lambda) over bar (n)f=3 317(-14) (-7) +/- 13 MeV, where the first quoted errors are our estimate of theoretical uncertainties of the method, which we consider conservative. The second uncertainties come from the present uncertainties in F pi = F and F pi / F0, where F (F0) is F pi in the exact chiral SU(2) (SU(3) limits. Combining the (Lambda) over bar (n)f=3 results with a standard perturbative evolution provides a new independent determination of the strong coupling constant at various relevant scales, in particular alpha(s)(m(Z)) 0: 1174+0010-0005 +/- 0: 001+0: 0005evol and alpha(nf)(s)=(3) (m(r)) = 0.308+007 +/- 004-0: 007 + 0: 002evol. A less conservative interpretation of our prescriptions favors central values closer to the upper limits of the first uncertainties. The theoretical accuracy is well comparable to the most precise recent single determinations of alpha(S), including some very recent lattice simulation determinations with fully dynamical quarks.